Prerequisite Skills
VOCABULARY CHECK
Use the diagram to name an example of the described
figure.
1.
A right angle
ANSWER
2.
AGC
A pair of vertical angles
ANSWER
BGC,
EGF
Prerequisite Skills
VOCABULARY CHECK
Use the diagram to name an example of the described
figure.
3.
A pair of supplementary angles
ANSWER
4.
BGC,
CGE
A pair of complementary angles
ANSWER
AGB,
BGC
Prerequisite Skills
SKILLS AND ALGEBRA CHECK
Describe what the notation means. Draw the figure.
5.
AB
ANSWER Segment AB
6.
CD
ANSWER Line CD
7.
EF
ANSWER
Length of segment EF
Prerequisite Skills
8.
GH
ANSWER Ray GH
SKILLS AND ALGEBRA CHECK
Prerequisite Skills
Solve the equation.
9. 3x + 5 = 20
ANSWER 5
10.
4(x – 7) = –12
ANSWER 4
11.
5(x + 8) = 4x
ANSWER –40
SKILLS AND ALGEBRA CHECK
Prerequisite Skills
SKILLS AND ALGEBRA CHECK
Name the postulate used. Draw the figure.
12. m
ABD + m
ANSWER
13.
ST + TU = SU
ANSWER
DBC = m
ABC
EXAMPLE 1
Describe a visual pattern
Describe how to sketch the fourth figure in the pattern.
Then sketch the fourth figure.
SOLUTION
Each circle is divided into twice as many
equal regions as the figure number.
Sketch the fourth figure by dividing a
circle into eighths. Shade the section just
above the horizontal segment at the left.
EXAMPLE 2
Describe a number pattern
Describe the pattern in the numbers –7, –21, –63,
–189,… and write the next three numbers in the
pattern.
Notice that each number in the pattern is three times
the previous number.
ANSWER
Continue the pattern. The next three numbers are
–567, –1701, and –5103.
GUIDED PRACTICE
for Examples 1 and 2
1. Sketch the fifth figure in the pattern in example 1.
ANSWER Graphic Required
GUIDED PRACTICE
for Examples 1 and 2
2. Describe the pattern in the numbers 5.01, 5.03, 5.05,
5.07,… Write the next three numbers in the pattern.
Notice that each number in the pattern is increasing
by 0.02.
5.01
5.03
+0.02
5.05
+0.02
5.07
+0.02
5.09
+0.02
5.11
+0.02
5.13
+0.02
ANSWER
Continue the pattern. The next three numbers are
5.09, 5.11 and 5.13
EXAMPLE 5
Find a counterexample
A student makes the following conjecture about the
sum of two numbers. Find a counterexample to
disprove the student’s conjecture.
Conjecture: The sum of two numbers is always
greater than the larger number.
SOLUTION
To find a counterexample, you need to find a sum that
is less than the larger number.
EXAMPLE 5
Find a counterexample
–2 + –3 = –5
–5 > –2
ANSWER
Because a counterexample exists, the conjecture is
false.
EXAMPLE 6
Standardized Test Practice
EXAMPLE 6
Standardized Test Practice
SOLUTION
Choices A and C can be eliminated because they
refer to facts not presented by the graph. Choice B is
a reasonable conjecture because the graph shows an
increase from 1990–2001, but does not give any
reasons for that increase.
ANSWER
The correct answer is B.
GUIDED PRACTICE
for Examples 5 and 6
5. Find a counterexample to show that the following
conjecture is false.
Conjecture: The value of x2 is always greater than
the value of x.
1
2
1
4
( )
2
=
>
1
4
1
2
ANSWER
Because a counterexample exist, the conjecture is
false
GUIDED PRACTICE
for Examples 5 and 6
6. Use the graph in Example 6 to make a conjecture
that could be true. Give an explanation that
supports your reasoning.
ANSWER
Conjecture: The number of girls playing soccer in
the year 2002 will increase over previous years;
the number of girls participate in soccer has
increased for the past 11 years.